Beck–De Loera–Develin–Pfeifle–Stanley conjecture on roots of Ehrhart polynomials

Let $P$ be a lattice $D$-polytope, and let its Ehrhart polynomial have complex roots. For a root $\alpha$, write $\Re(\alpha)$ for its real part. Beck–De Loera–Develin–Pfeifle–Stanley conjecture. All roots $\alpha$ of Ehrhart polynomials of lattice $D$-polytopes satisfy

$$-D \leq \Re(\alpha) \leq D-1.$$

The conjecture concerns the location of Ehrhart-polynomial roots in a vertical strip determined by the dimension of the polytope; the source gives no resolution status, so its status is recorded as open.